C₁₇×#7214 #16864958

order	4352
nilpotency class	4
isoclinism	isoclinic class of #7213
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7214

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#342
commutator	C₂²×C₄	C₄²×C₁₇
Frattini, cosocle	C₂×#117	C₂²×C₁₇
prime radical	C₂⁴×C₁₇	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#117 ◁ G

290 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,22)(21,24)(23,25)(26,27)(28,36)(29,40,41,33)(30,34)(31,35)(32,37,44,50)(38,48)(39,49)(42,53,54,46)(43,47)(45,51,55,57)(52,56);(19,22,24,23)(26,28,30,38,31,39,43,52)(27,32,34,45,35,44,47,55)(29,37,42,51,41,50,54,57)(33,36,46,48,40,49,53,56)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 202);